We study a distribution of times of the first arrivals to absorbing targets in turbulent diffusion, which is due to a multiplicative noise. Two examples of dynamical systems with a multiplicative noise are studied. The first one is a random process according to inhomogeneous diffusion, which is also known as a geometric Brownian motion in the Black-Scholes model. The second model is due to a random processes on a two-dimensional comb, where inhomogeneous advection is possible only along the backbone, while Brownian diffusion takes place inside the branches. It is shown that in both cases turbulent diffusion takes place as the one-dimensional random process with the log-normal distribution in the presence of absorbing targets, which are characterized by the Lévy-Smirnov distribution for the first hitting times.

中文翻译：

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乘性噪声引起的湍流扩散中的击中时间

我们研究了湍流扩散中初次到达目标的时间分布，这是由于倍增噪声引起的。研究了具有乘性噪声的动力系统的两个例子。第一个是根据不均匀扩散的随机过程，在Black-Scholes模型中也称为几何布朗运动。第二种模型是由于二维梳状结构上的随机过程所致，其中仅沿着骨架可能发生不均匀对流，而布朗扩散发生在分支内部。结果表明，在两种情况下，湍流扩散都是一维随机过程，在存在吸收目标的情况下呈对数正态分布，其特征是第一次命中时的Lévy-Smirnov分布。